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A mechanical model of Brownian motion

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Abstract

We consider a dynamical system consisting of one large massive particle and an infinite number of light point particles. We prove that the motion of the massive particle is, in a suitable limit, described by the Ornstein-Uhlenbeck process. This extends to three dimensions previous results by Holley in one dimension.

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Authors and Affiliations

  1. Department of Mathematics, Rutgers University, 08903, New Brunswick, NJ, USA

    D. Dürr, S. Goldstein & J. L. Lebowitz

Authors
  1. D. Dürr
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  2. S. Goldstein
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  3. J. L. Lebowitz
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Additional information

Communicated by A. Jaffe

On leave of the Institut für Theoretische Physik I der Universität Münster. Supported by a Nato fellowship

Supported by NSF Grant, No. PHY 78-03816

Supported by NSF Grant, Phy 78-15920

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Dürr, D., Goldstein, S. & Lebowitz, J.L. A mechanical model of Brownian motion. Commun.Math. Phys. 78, 507–530 (1981). https://doi.org/10.1007/BF02046762

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  • DOI: https://doi.org/10.1007/BF02046762

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